# Behavior of transitional plane fountains in linearly-stratified environments

Inam, Mohammad Ilias
(2016)
*Behavior of transitional plane fountains in linearly-stratified environments.*
PhD thesis, James Cook University.

PDF (Thesis)
Restricted to Repository staff only until 10 July 2020. |

## Abstract

Fountains, also called negatively buoyant jets, are widely present in environmental settings and practical applications, such as natural ventilation, volcanic eruption, cumulus clouds, reverse cycle air conditioning, to name just a few. A good understanding of the behaviour of fountains in homogeneous ambient fluids has been attained attributed to extensive past studies since the 1950s. However, the understanding of the behavior of fountains in stratified fluids, in particular that of plane fountains, is currently lacking, which motivates this study.

The behavior of plane fountains in linearly-stratified fluids is mainly governed by the stratification of the ambient fluid, represented by the dimensionless temperature stratification parameter (s), along with the Reynolds number (Re) and the Froude number (Fr). In this study, a series of three-dimensional DNS runs were carried out using ANSYS FLUENT 13 for transitional plane fountains in linearly-stratified fluids with Fr, Re and s varying in the ranges of 1 ≤ Fr ≤ 10, 10 ≤ Re ≤ 300 and 0 ≤ s ≤ 0:7 to examine the effects of these governing parameters on the transient behavior of these transitional plane fountains. In particular, the effects of Fr, Re and s on the symmetric-to-asymmetric transition, initial and time-averaged maximum fountain penetration height, characteristics of bobbing and flapping motions, and thermal entrainment are analyzed and quantified with the obtained DNS results and compared to the scaling relations obtained by dimensional analysis for weak plane fountains in linearly-stratified fluids, at Fr = O(1).

Over the ranges of Fr, Re and s considered in this thesis, it was found that a transitional plane fountain in a linearly-stratified fluid can be either symmetric or asymmetric. In an asymmetric plane fountain, the fountain ow behavior becomes asymmetric at the later developing stage, characterized by bobbing and flapping motions, although at the early developing stage it is symmetric and no bobbing and flapping motions are present. In a symmetric plane fountain, however, the fountain ow remains symmetric all the time without the presence of bobbing and flapping motions. The DNS results show that plane fountains remain symmetric for all times at a lower Fr or Re value or at a higher s value. On the contrary, when Fr or Re is large or the stratification is weak with a small s, plane fountains will remain symmetric only in the early developing stage and will become asymmetric at the later, fully developed stage. The regime maps to distinguish the symmetric plane fountains from the asymmetric ones were developed in terms of Fr, Re and s. It was observed that the critical Fr and Re values for the asymmetric transition move up when s increases, due to the stabilizing effect of stratification; on the other hand, the critical Re value for the asymmetric transition reduces when Fr increases at lower Fr values, but becomes essentially independent of Fr when Fr is high.

For symmetric plane fountains in linearly-stratified fluids, the DNS results show that in general Fr has a much stronger effect on the maximum fountain penetration height and the associated time than s does, whereas the effect of Re is negligible. In addition, intrusion is an important integral part of the fountain behavior for these symmetric plane fountains, and hence often has a substantial effect on the fountain behavior, in particular at the later, fully developed stage. This is because the formation and the subsequent movement of the intrusion change the stratification condition of the ambient fluid, which results in a smaller negative buoyant force that the fountain fluid experience. This is particularly prominent at small Fr values or very strong stratifications under which the maximum fountain penetration height is significantly restricted. Empirical correlations to quantify the effects of Fr, Re and s on the maximum fountain penetration height and the associated time, as well as the intrusion height and velocity were developed using the DNS results.

For asymmetric transitional plane fountains in linearly-stratified fluids, the DNS results show that both the initial and time-averaged maximum fountain penetration height and the time to attain the initial maximum fountain penetration height increase monotonically with Fr, apparently due to the stronger momentum flux of the injected fountain fluid, whereas on the contrary, due to the stronger negative buoyancy force at higher s values, these bulk fountain behavior parameters reduce with s , although the effect of Re is found to be negligible. The DNS results also demonstrate that the extent of both the bobbing and flapping motion increases with Fr and Re but decreases with s. The bobbing motions are predominated by a single dominant frequency over the ranges of Fr, Re and s considered, and it is found that this dominant bobbing frequency decreases monotonically with Fr, but increases with s. The flapping motions occur along both the X direction (i.e. perpendicular to the slot) and the Y direction (i.e. along the slot). The flapping motions along the X direction are also predominated by a single dominant frequency, and similar to the bobbing motions, this dominant flapping frequency also decreases monotonically with Fr, and increases with s. The effect of Re on the dominant frequencies for the bobbing motions and the flapping motions along the X direction is found to be insignificant. On the other hand, the flapping motions along the Y direction are more chaotic and fluctuate with multiple dominant frequencies.

For asymmetric transitional plane fountains in linearly-stratified fluids, the DNS results further demonstrate that thermal entrainment is one of the major features of plane fountains and plays a key role for the symmetric-to{asymmetric transition and the turbulent mixing process in asymmetric fountains. Over the parameter ranges considered, it is observed that thermal entrainment in general has a negligible effect on the core region of the injected fountain fluid, but plays a key role in the downflow, in particular at the interface between the upflow and the downflow, as well as at the interface between the downflow and the ambient fluid, which becomes more dominant and stronger at the later ow developing stages. At the early developing stage, thermal entrainment occurs mainly in a very thin layer which is the interface of the fountain top and the ambient fluid. It is also observed that thermal entrainment decreases with height. Thermal entrainment is further found to be characterized by several representative average thermal entrainment coefficients.

The DNS results were used to develop a series of empirical relations to quantify the individual and combined effects of Fr, Re and s, over their ranges considered, on the bulk fountain behavior parameters, including the initial and time-averaged maximum fountain penetration heights, the time to attain the initial maximum fountain penetration height, the onset time for the symmetric-to-asymmetric transition, the dominant frequencies of the bobbing and flapping motions, and several representative thermal entrainment coefficients. Notably, it is found that the scaling relations developed by Lin & Armfiled (2002) for weak plane fountains in linearly-stratified fluids, at Fr = O(1), in general also work well for the asymmetric transitional plane fountains in linearly-stratified fluids considered in this thesis, which have higher Fr values. Similarly, it is also found that this is true for the symmetric plane fountains considered in this thesis as well.

Item ID: | 49460 |
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Item Type: | Thesis (PhD) |

Keywords: | asymmetry, computational fluid dynamics, direct numerical simulation, fluid mechanics, fluidisation, Froude number, maximum fountain height, penetration heights, plane fountains, Reynolds number, stratification, stratified fluids, transitional flow |

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Additional Information: | Embargoed until 10 July 2020. Publications arising from this thesis are available from the Related URLs field. The publications are: Inam, Mohammad Ilias, Lin, Wenxian, Armfield, S.W., and He, Yinghe (2015) Asymmetry and penetration of transitional plane fountains in stratified fluid. International Journal of Heat and Mass Transfer, 90. pp. 1125-1142. Inam, Mohammad Ilias, Lin, Wenxian, Armfield, S.W., and He, Yinghe (2016) Correlations for maximum penetration heights of transitional plane fountains in linearly stratified fluids. International Communications in Heat and Mass Transfer, 77. pp. 64-77. |

Date Deposited: | 26 Jun 2017 00:24 |

FoR Codes: | 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 60% 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics @ 40% |

SEO Codes: | 97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 100% |

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